Kurdish militias in the besieged northern Syrian town of Kobani claim to be making gains against Islamic State (IS) militants.

Rafiq Baradar, a commander with the Kurdish Peoples Protection Units (YPG) in Kobani, painted a very positive picture of the situation, telling the "Los Angeles Times" on November 17 that IS was close to defeat.

“They will probably be finished in four or five days,” Baradar said in an interview in the Turkish border town of Suruc.

Baradar also said that only around 250 IS militants remain inside Kobani, in the southeastern corner of the town.

Other Kurdish sources, however, have been rather more cautious in their assessment of the situation in Kobani.

Anwar Muslim, a Kurdish political leader in Kobani, told the "Los Angeles Times" that IS was retreating but “not retreating as much as we want.”

The Kurdish claims came amid reports of huge explosions in Kobani on November 17, which appeared to be the result of U.S.-led air strikes targeting IS militants in the town.

Photographs and video footage of huge plumes of smoke alleged to be rising from the sites of the explosions were widely shared on social media.

The strikes “destroyed seven ISIL (another acronym for IS) fighting positions, suppressed another ISIL fighting position, destroyed four ISIL staging areas, and struck one tactical ISIL unit,” the U.S. Central Command said in a press release.

Syrian Kurdish YPG militias have been battling IS militants in and around Kobani for weeks, bolstered by U.S.-led air strikes and -- more recently -- by the arrival of Iraqi Kurdish Peshmerga forces. As well as besieging Kobani, IS militants have captured a number of villages around the town.

Are the Kurdish claims of gains -- possibly even dramatic gains -- accurate?

The nature of the fighting in and around Kobani has meant that it is not possible to get a very clear picture of the state of the battle for the town. Kurdish militias tend to report dramatic gains, while IS militants are either silent or also report dramatic gains. However, there have been indications that Kurdish militias have been making some advances in the battle for Kobani.

One such indication came on November 12 when a Kobani town official and a British-based monitoring group both reported that Kurdish militias had blocked a road that IS militants were using to resupply their forces inside Kobani. Idris Nassan, a local official, told Reuters that the Kurds had retaken the hill of Mistanour and the road running alongside it.

This report was later confirmed by a Chechen IS militant, who admitted via social media on November 14 that Kurdish forces had, indeed, taken the hill.

The militant, who claims to be an ethnic Chechen from Germany and who is a member of the Chechen IS faction Katibat al-Aqsa, said that Arabic-speaking IS militants had retaken the position overnight on November 12-13.

According to the militant, who described the news of the hill’s capture by the Kurds as “alarming,” the hill is strategically important and the Kurdish capture of it “blocked the road for the mujahedin (IS militants) to enter and exit the town.”

While the report from the IS militant cannot be confirmed, it does contain interesting information.

In the first place, it is very unlikely that IS militants would report that the Kurds had retaken an important position unless it were true.

The Chechen IS militant also claimed that the Kurds had been assisted in their capture of the hill by “American intelligence” and that the Kurdish forces had carried out their operation in the “dead of night,” a sign that Kurdish militias are able to strategically outmaneuver IS to make gains.

However, the militant says that the hill switched hands twice before IS managed to recapture it, an indication that while the Kurds are making advances, these involve heavy fighting, likely with losses on both sides.

-- Joanna Paraszczuk

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"Under The Black Flag" provides news, opinion, and analysis about the impact of the Islamic State (IS) extremist group in Syria, Iraq, and beyond. It focuses not only on the fight against terrorist groups in the Middle East, but also on the implications for the region and the world.